Parfit's Brain Experiment (Shoemaker)
Personal identity is not relevant.
David Shoemaker. "Personal Identity and Ethics." The Stanford Encyclopedia of Philosophy (Spring 2012 Edition).
By way of explanation, consider the case Parfit uses in support of his claim that identity is not what matters: fission (Ibid., 254–255). Suppose both of my brain hemispheres are functional duplicates of the other, and that each of my other two triplet brothers has suffered irreversible brain damage. A brilliant neurosurgeon can transplant one of my brain hemispheres into each [of my two] brother[s], and so each survivor (we will stipulate) will be fully psychologically continuous with me upon waking up. What has happened to me? If we lack the “no branching” clause, we are forced to say that, because both brothers are psychologically continuous with me, they [If my two brothers] are both me. But then (given the transitivity of identity) both survivors would also have to be identical to each other, which seems obviously false (although see Belzer 2005 for doubts about this assertion). So to avoid violating this transitivity requirement, we simply have to stipulate in our criterion of personal identity that, if the relations in which identity consists may hold one-many, they must obtain uniquely for identity itself to obtain. But then what has happened to me in fission? It seems I cannot survive as both, so the identity relation does not obtain between me and the survivors. In addition, there simply is no non-arbitrary reason why it should obtain between me and just one of the survivors, so the only remaining option is that I do not survive fission (see Parfit 2001, 42; see also Brink 1997b, 140–141). But is this like an ordinary case in which I don't survive, i.e., like death? Clearly not: both survivors will seem to remember my thoughts and experiences, they will fulfill intentions I had in action, they will have the same beliefs/desires/goals as me, and their characters will be exactly like mine. Indeed, it will be just as if I had survived. Everything that matters in ordinary survival (or nearly everything), therefore, is preserved in fission, despite the fact that the identity relation is not. What this must mean, then, is that the identity relation just is not what matters (or is not what matters very much) in survival; instead, what matters has to consist in psychological continuity and/or connectedness (what Parfit calls “Relation R”). As long as that relation holds between me-now and some other person-stage — regardless of whether or not it holds one-one — what happens to me is just as good as ordinary survival. Call this the Identity Doesn't Matter (IDM) view.